As noted previously, alternating between pressurization of the clogged line followed by applying a rough vacuum, results in gas generation on the atmospheric side (gauge side when connected to the gauge) of the obstruction results.  My initial, optimistic, interpretation was that the ice plug was getting "drawn" slowly up the sensing tube and making contact with relatively warm surfaces, thus melting the leading portion of the plug.  Considering the repeatable phenomenon of watching the gas pressure build up on the gauge only to have it fluctuate as if the accumulated gas was being released via some unknown path, I now have a new, more pessimistic, picture in my head (see attached sketch).   Maybe the ice plug is irregular in shape and not it complete contact with the large diameter aluminum tube wall such that it gets rocked, cocked, tilted etc. by the pushing and pulling of applying pressurized UHP N2 followed by vacuum pumping.  If this is happening then small amounts of LN2 can leak past and turn to gas and this is the source of the gas not the vanishing ice plug.  Since the gauge end of the sensing tube is closed, the pressure build up of GN2 can then escape past the ice obstruction back to the LN2 side.  This is consistent with the observations.  Note in the sketch that water ice is denser that LN2 and would be expected to concentrate at the bottom of the pump.  Also, once formed, it has no place to go.  It is too big to enter into the small I.D. of the SS sensing tube or make it past the "hard" 90 degree aluminum tube elbow.  

My wife thinks I'm Christmas shopping!